{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example from Think Stats\n",
    "\n",
    "http://thinkstats2.com\n",
    "\n",
    "Copyright 2019 Allen B. Downey\n",
    "\n",
    "MIT License: https://opensource.org/licenses/MIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import random\n",
    "\n",
    "import thinkstats2\n",
    "import thinkplot\n",
    "\n",
    "from matplotlib import MatplotlibDeprecationWarning\n",
    "\n",
    "from warnings import simplefilter\n",
    "simplefilter('ignore', MatplotlibDeprecationWarning)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Central Limit Theorem\n",
    "\n",
    "If you add up independent variates from a distribution with finite mean and variance, the sum converges on a normal distribution.\n",
    "\n",
    "The following function generates samples with difference sizes from an exponential distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def MakeExpoSamples(beta=2.0, iters=1000):\n",
    "    \"\"\"Generates samples from an exponential distribution.\n",
    "\n",
    "    beta: parameter\n",
    "    iters: number of samples to generate for each size\n",
    "\n",
    "    returns: list of samples\n",
    "    \"\"\"\n",
    "    samples = []\n",
    "    for n in [1, 10, 100]:\n",
    "        sample = [np.sum(np.random.exponential(beta, n))\n",
    "                  for _ in range(iters)]\n",
    "        samples.append((n, sample))\n",
    "    return samples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function generates normal probability plots for samples with various sizes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def NormalPlotSamples(samples, plot=1, ylabel=''):\n",
    "    \"\"\"Makes normal probability plots for samples.\n",
    "\n",
    "    samples: list of samples\n",
    "    label: string\n",
    "    \"\"\"\n",
    "    for n, sample in samples:\n",
    "        thinkplot.SubPlot(plot)\n",
    "        thinkstats2.NormalProbabilityPlot(sample)\n",
    "\n",
    "        thinkplot.Config(title='n=%d' % n,\n",
    "                         legend=False,\n",
    "                         xticks=[],\n",
    "                         yticks=[],\n",
    "                         xlabel='Random normal variate',\n",
    "                         ylabel=ylabel)\n",
    "        plot += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following plot shows how the sum of exponential variates converges to normal as sample size increases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.PrePlot(num=3, rows=2, cols=3)\n",
    "samples = MakeExpoSamples()\n",
    "NormalPlotSamples(samples, plot=1,\n",
    "                  ylabel='Sum of expo values')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The lognormal distribution has higher variance, so it requires a larger sample size before it converges to normal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def MakeLognormalSamples(mu=1.0, sigma=1.0, iters=1000):\n",
    "    \"\"\"Generates samples from a lognormal distribution.\n",
    "\n",
    "    mu: parmeter\n",
    "    sigma: parameter\n",
    "    iters: number of samples to generate for each size\n",
    "\n",
    "    returns: list of samples\n",
    "    \"\"\"\n",
    "    samples = []\n",
    "    for n in [1, 10, 100]:\n",
    "        sample = [np.sum(np.random.lognormal(mu, sigma, n))\n",
    "                  for _ in range(iters)]\n",
    "        samples.append((n, sample))\n",
    "    return samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.PrePlot(num=3, rows=2, cols=3)\n",
    "samples = MakeLognormalSamples()\n",
    "NormalPlotSamples(samples, ylabel='sum of lognormal values')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Pareto distribution has infinite variance, and sometimes infinite mean, depending on the parameters.  It violates the requirements of the CLT and does not generally converge to normal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def MakeParetoSamples(alpha=1.0, iters=1000):\n",
    "    \"\"\"Generates samples from a Pareto distribution.\n",
    "\n",
    "    alpha: parameter\n",
    "    iters: number of samples to generate for each size\n",
    "\n",
    "    returns: list of samples\n",
    "    \"\"\"\n",
    "    samples = []\n",
    "\n",
    "    for n in [1, 10, 100]:\n",
    "        sample = [np.sum(np.random.pareto(alpha, n))\n",
    "                  for _ in range(iters)]\n",
    "        samples.append((n, sample))\n",
    "    return samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x720 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.PrePlot(num=3, rows=2, cols=3)\n",
    "samples = MakeParetoSamples()\n",
    "NormalPlotSamples(samples, ylabel='sum of Pareto values')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the random variates are correlated, that also violates the CLT, so the sums don't generally converge.\n",
    "\n",
    "To generate correlated values, we generate correlated normal values and then transform to whatever distribution we want."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def GenerateCorrelated(rho, n):\n",
    "    \"\"\"Generates a sequence of correlated values from a standard normal dist.\n",
    "    \n",
    "    rho: coefficient of correlation\n",
    "    n: length of sequence\n",
    "\n",
    "    returns: iterator\n",
    "    \"\"\"\n",
    "    x = random.gauss(0, 1)\n",
    "    yield x\n",
    "\n",
    "    sigma = np.sqrt(1 - rho**2)\n",
    "    for _ in range(n-1):\n",
    "        x = random.gauss(x * rho, sigma)\n",
    "        yield x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm\n",
    "from scipy.stats import expon\n",
    "\n",
    "def GenerateExpoCorrelated(rho, n):\n",
    "    \"\"\"Generates a sequence of correlated values from an exponential dist.\n",
    "\n",
    "    rho: coefficient of correlation\n",
    "    n: length of sequence\n",
    "\n",
    "    returns: NumPy array\n",
    "    \"\"\"\n",
    "    normal = list(GenerateCorrelated(rho, n))\n",
    "    uniform = norm.cdf(normal)\n",
    "    expo = expon.ppf(uniform)\n",
    "    return expo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def MakeCorrelatedSamples(rho=0.9, iters=1000):\n",
    "    \"\"\"Generates samples from a correlated exponential distribution.\n",
    "\n",
    "    rho: correlation\n",
    "    iters: number of samples to generate for each size\n",
    "\n",
    "    returns: list of samples\n",
    "    \"\"\"    \n",
    "    samples = []\n",
    "    for n in [1, 10, 100]:\n",
    "        sample = [np.sum(GenerateExpoCorrelated(rho, n))\n",
    "                  for _ in range(iters)]\n",
    "        samples.append((n, sample))\n",
    "    return samples\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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8DsA9AIZmXxORwSRSefU1l9S2YK4jMpAXm5oFbVk2DJvF4Fdki4e5jsgAqn30hLOdgvNOKWUN9XX+a3SOh4h09MreafX1qqWBLkbSk5jriAzkxanG/s3zuZz2VDDXERlAJNtYleZ1GHvkUzu3Aw8IIe4QQlwnjNweiWjAJdJ5TE1HAQAmkwnnrl/a5Yh6DnMdkUFE0iUcitVXbFhMAluWD3c5IkNhriMygKOZRt+NJR5jr0prp+A8G8CDAH4bwJQQ4u+EEJfrGxYRddrLuw+rrzesmYDTwT2cx2GuIzKIF4+bvem0mbsYjeEw1xEZwLF0o+Cc9PZ5wSmlLEgpfyClvAXAeQC8qC/DICIDeem1RsF53jnLuxhJb2KuIzKO5nEo21b5uhiJ8TDXEfW+YqWGeL7e38skgHGPsR8StLXDXghxlRDiawBeRH1I8Lt1jYqIOkpRFGxvKjjP38iCcz7MdUS9L5krY18oC6B+IXbeShacp4q5jqi3zWQa+zdH3TZYDd6mdsEdqEKIAwBeBvADAH8gpczpHhURddS+QxFk8/WlGT6PCysn2TDoeMx1RMbQ/HRz/RIPPA5rF6MxHuY6ot53tGk57RKDL6cF2utSu1VKmdY9EiLSzUtN+zfP27Ac7BMxL+Y6IgNo3r/J7rSnhbmOqMf10/5NoL09nExKRAb30u5D6uttG7icdj7MdUS9L1usYs+xjHq8jctpTxlzHVFvK9cURHKNJbUTBu9QC7S5h5OIjCuTK2LfwTAAQADYevay7gZERHSath9KYm4W+poxN0bcxm6kQUR0vMOJovp61G2F3WL8cs3YU0SJaEHb9xzB7PUZ1q4cg8ft6Go8RESn64UDjeW0F3A5LRH1CUVKHEoUsWMmg+lUYzltPzzdBE5ScAohPnOyL0opb+98OETUac37N7dtWNHFSHoTcx2RMRTLNeyabqwG5TiUU8NcR9RbFCmxN5LHwUQB06kSyjWl5TNnBVxdiKzzTvaE07NoURCRLqSUeFlTcHL/5jyY64gM4JUjKVRn19Mu9zsx5uVqjVPEXEfUQx57I4E9kfmbRK/2O7F10tP/TzillF9YzECIqPMOHo0hmckDAIZcdqxdEexyRL2HuY6od+VLVfzijThePpTEnqONZkHnr+Zy2lPFXEfUO16P5lqKTZfVjHVBFzZPDMFj769dj+3M4XQA+CiATagPBwYASCk/omNcRNQBL+5qPN3ces5ymEzG33iuF+Y6ot5SUyT+v3tfw0yy2PIe92+ePuY6ou5SpMTTU0nNuVu2jCPotvbt2Lp2rj7vAjAB4C0AHgOwDEDmpN8gop7QPA7lfC6nXQhzHVEPORzLtxSby/xOfOjKVZgccXYpqr7AXEfUReFMGYVKY7/me7dNYGzI1rfFJtBel9q1UspbhRDvlFJ+WwjxLwB+rndgRHRm8oUyXjsQUo+3nsOCcwHMdUQ9ZH/TcrNzJj340BWrMNon+5m6jLmOqIumEgX19Tljbgw7rF2MZnG0U3BWZn9PCiE2A5gBsEq3iIjojJTKFRw+lsBzO6agKPU7aKuWjmLE2x+dznTEXEfUI6o1Bfe+eFQ93rrCx2Kzc5jriLroYFPBuWpAVmu0U3DeIYQYAfA5APcAGALwx7pGRURtK1equO+Jndg7FcKhozEci6TUuZtzuJy2Lcx1RD3iq/fvQ6ZYVY/PGnN3MZq+w1xH1CXJQgWJQj23mU0CS4cH40baggWnlPJbsy8fA7BG33CI6FR98wdP4NHn9pzwfQHg8gvWLl5ABsVcR9QbShXtvM0RtxUr+mQWXS9griPqjly5hof3xdXj5cMOWM2D0czxhAWnEOI2KeV3TzQomAOCibpv+54jLcWmALAkOIwVkwGsnPTjwk0rsXIy0J0ADYC5jqi3lKra4ed/+I5zYBmQizI9MdcRdYeUEm/ECnh6Kol8paaeP2eAVm6c7Ann3H+F+QYFH79ij4gWWbFUwTf+7TH1+IKNK/Hut16A5UtGYLf1/wb0DmKuI+oh5aaCc8Rt5d7NzmGuI1pk06kinjmYRDRXUc8JAJes9GGVfzD2bwInKTillN+cffmglPKp5veEEJfpGhURLej79z2PcLzeyd7ttOOT77sKPg+XnZ0q5jqi3lKpNQpOm4VPNjuFuY5o8VQViUf2xfBGrKA5b7eYcOP6AJYOO07wzf7UTib/2zbPEdEi2XcwjHsf2a4ef/jmS1lsnjnmOqIeUKk1HrbZuJRWD8x1RDrbcSyjKTbNJoHzJj1499aJBYtNKSWq1epJP2M0J9vDeQmASwEEj1vv7wVg1jswIppftVrD1/7tMXX905b1S3H1xeu7GpORMdcR9ZbmJbVWPuHsGOY6Iv2Uqgp2hbIIZcuIZMvIlRt7NQWA9543gSH7wsNBKpUKQqEQpJRYtmwZhBA6Rr14TvY3t6HeKtsC7Xr/NIBf1zMoIjqxex55BQePxgAAVosZH3/3lX2TkLqEuY6oh1SqXFKrE+Y6Ih1IKfGzPVEcS5fmff+6dYG2is1sNotwOKzOUI9GowgGgx2NtVtOtofzMQCPCSH+WUp5cBFjIqITePrlN/D9nz2vHr/37RdjSXC4ixEZH3MdUW/RPOHkktqOYa4j0seuUK6l2LSYBEbdNqwccWD1As2BFEVBNBpFOp3WnLdYFi5SjaKdv4ldCHEHgFXNn5dSXqtXUESkVa5U8e3/fAY/e3Knem71slG846otXYyq7zDXEXVRulDBQzvDeGR3WD1nNXP1hg6Y64g6JF+u4dlDSfV4w5gbW5Z44HNaYGpj9Vm5XMbMzAzK5bJ6zmKxYGJiAg5H/zQWaqfg/CGAbwD4FoDaAp8log6TUuL2f34Qv3x1Sj0XHPHg0795Pcy8+99JzHVEXVCq1PDD547gyb1RVGva6Ryrg4Mzp24RMdcRdcihZFFtdDbssOCy1SOwmBYuNKWUyGQyiEQikLKR94aGhhAMBmE299e26nYKzqqU8uu6R0JE85qJpjXF5pvPXY1Pvu9quJ2cTddhzHVEiyRbrOJwPI/peAH/9uzhlvfHvHbcuGUcV53TG/uXpJT9tFeeuY6oQ8pNY5yW+xxtFZuKoiASiSCTyajnhBAYHR2F1+vtp1yjaqfgvFcI8UkAdwNQFyhLKeO6RUVEqj0HZtTXW9Yvxe9/5Ma+TEY9gLmOSGeRdAl/98A+TCcK875vNQt89OrVOH/lCExtXLjpTUqJVCqFfD6PJUuW9EvuZa4j6pDmp5PmNvJDqVTCzMwMKpWKes5qtWJiYgJ2e/8+SGin4PzN2d//oOmcBLCm8+EQ0fFeayo4N69b2i8XPL2IuY5IJ8/ui+GFAwm8dDB5ws/4XFb82a2bYbf2xlKyYrGISCSCUqlek2UyGXi93i5H1RHMdUQdMp1qNAs62eXZ3M2rWCymKVI9Hg+CwSBMpv7eIrVgwSmlXL0YgRDR/F47EFJfn71qvIuR9DfmOqLOOxDJ4WsP7kMiV2l5zz9kw4ZJD5b7XVjqd+KssaGeGINSq9UQj8eRSqU05zOZDDwej+Fv+jHXEZ25XLmGJw8kcChZVM/ZTtBXo1arIRwOI5fLqeeEEBgbG4PH45n3O/1mwYJTCOEC8BkAK6SUvyWEWAfgbCnlf+keHdGAyxVKOHKsvsrJJATWrRzrckT9i7mOqLOklLjj4f3zFptXnj2KD16xavGDOgkpJXK5HCKRCGq1pqHtQsDv98Pn8xm+2ASY64jORFWReO5QCq+Fsygf1+Rswmtr+XyhUEAoFEK1WlXP2e12jI+Pw2Zr/Xy/amdJ7Z0AXgBw6ezxEdQ7nDExEels71QYc+ls1bJROOzWrsbT55jriDpofziHSEY7m+6jV63GhkkPfO7eutCqVCqIRCLI5/Oa8y6XC8FgEFZrX+Ve5jqi0/TUVAK7QznNubMCLmyacGPS2xhjIqVEIpFAPK7dGj08PIzR0dG+uHl1KtopOM+SUr5HCPFeAJBSFsSg/Vci6pJd+46qr89ZzeW0OmOuI+qg1441OjAu8zvxRzed0zP7M+dIKZFMJhGPx7XNP8xmBINBuN3ufrwwZK4jOk3NezYB4B0bg1g2rJ2XWa1WEQqFUCg0mqOZTCaMj4/D7R7MUU/tFJxlIYQT9Q3lEEKchaauZkSkj1SmgJ89uVM93nDWki5GMxCY64g66LWjafX1W7ZM9FyxWSgUEIlENAPXgfoTCL/f33dz8Jow1xGdplK1MQblAxdMwm3T5ol8Po9QKKRZlu9wODAxMQGLpZ2yqz+18zf/EwA/A7BcCPE9AJcB+JCeQRENOiklvvWjJ5Ev1i+EJoPDuHjzqu4G1f+Y64g66GC0sTx1/ZKhLkaiVavVEIvFkE6nNeftdjuCwSAcDscJvtk3mOuITpGUEvvjBU3B6WhqcialRDweRyKR0HxvZGQEfr+/H1dKnJJ2utQ+IIR4EcCbAQgAvyuljOoeGdEAu/fRV/D0S2+oxx945yWwWPr2bntPYK4j6qxy04XZsLP7eyCllMhkMojFYi1NgQKBAIaHhwfiopC5jujU1BSJu18NIdrUAM1mNsE8Oyu4UqkgFAqhWGx0rDWbzRgfH4fL5Vr0eHtRu892HQASs5/fKISAlPJx/cIiGlw79k7jrh8/qx7fcOkGXLxlVfcCGizMdUQdoCgSVaW+J1IIqBdm3VIulxGJRDR7qgDA7XYjGAwO4lI35jqiNr06k9UUmwDwphXDAIBsNotwOAxFadxgc7lcGBsbG8S8ckLtjEX5MoD3ANgJYO6/pgTAxETUYcciKXz+7+9Vj9etHMNHb7m8ixENDuY6os4pVBpPEK1mU9eeHCqKgmQyiUQioWkKZLFY1KZAg4a5jqh9VUXihSPa5fc3bQxiiceGSCTSMq83EAj0zQilTmqn9H4X6vOZuKGcSCeZXBFf+c5DePm1w5rzf/CRG2HtsUYbfYy5jugMKIrEE3uieHU6hWNNw9DHvPauxJPP5xGJRFCpaJ9M+Hw++P1+mEzzD2kfAMx1RG06kiyiXKvfl7FbTPjgBZOoVSs4cuSIpuGYxWLBxMTEIOwBPy3tFJz7AVjBDmZEupgOJ/Hnd9yHYxHtXbKzV08g4OudRhsDgLmO6AzsOJzCXU8dbDm/zO9c1DhqtRqi0SgymYzmvMPhQDAYhN3enQK4hzDXEbVhKl7A/Xsb25sDLity2QwikYhmxYTb7cbY2Fg/d7Y+Y+0UnHkALwshHkJTcpJSfkq3qIgGxCt7juAv/+l+tRstAKxY4kfA58ZvvO2iLkY2kJjriM7A0WSh5dyY144bt0wsyp8vpUQ6nUYsFtPspzKZTAgEAvB6vVzmVsdcR7SA/bE87t8bU4+llBi3lhEON5bXCiEwOjrK3NKGdgrOe2Z/EVEHPfD0LtzxgyegzN4ls1rM+NQHrsWl553V5cgGFnMd0RlQGjf8cfn6Ufz6xcvgtpsX5UKsVCohEoloukQCwNDQEEZHR9m8Q4u5jmge8XwFzx5MIpQta8afuK0Cm4aq8JoaDwesVismJia4YqJN7YxF+bYQwgZg/eypPVLKysm+Q0QnNx1O4pvffxxz12cjXhc++9/eirUrx7oa1yBjriM6M9Va4wLN57ZiyKF/kacoChKJRMvsO6vVimAwyJEE82CuI9JKF6t45mASB+LHrdKQEpVqFZt8CrxN6czj8SAYDA7yPvBT1k6X2qsBfBvAFOrzmpYLIX6T7bOJTt+re6fVYnP5xAg+94m3c79mlzHXEZ2Z5iecizEGJZfLIRKJoFqtqueEEPD5fBgZGeHF4Akw1xHVpYtVPL4/jiOp1u3MUkqYa2Vs8irwWuu5RAiBYDAIr9e72KEaXju3H/8awI1Syj0AIIRYD+BfAVygZ2BE/Ww6nFRfX37BOhabvYG5jugMpAvaoeh6qVariEajyGazmvMOhwNjY2Ow2Wy6/dl9grmOBt5MuoR7d0VQa2r+AwArfA4s91hgKSZhkRJC1HOZzWbDxMQE88tpaqfgtM4lJQCQUu4VQlh1jImo7x2ZaSz/Wjbu62Ik1IS5jugM7DnW6Aq7Ktj5+ZZSSqRSKcTj8ZamQKOjo/B4PGzc0R7mOhp4Lx1NtxSbN6zzw28uIxabbRY0m0/Nlg88AAAgAElEQVSGh4cRCAS4auIMtFNwPi+E+EcAd80evx/AC/qFRNT/mp9wLpsY6WIkp09KiUql0k93+5jriE5TLFtCOF1flmY1C6wZ62zBWSqVEA6HUSppl755PB6Mjo5yHMGpYa6jgRbLlXEw0Wgwdu6SIWwacyGXjCGWz6vnTSYTxsbGMDTEVWhnqp2C8xMAfhvAp1Bf6/84gK/pGRRRPyuWKogm6kvBTCYTJgLG2gsgpUQ+n1dHD6xYsaJf7vox1xGdphenGjfR1k14YO3QklpFURCLxZBKaecUW61WjI2Nwelc3BmffYK5jgaSlBKhTBkPvxFXz404rdgatCEcOoparaaedzgcGB8fh9XKh/+d0E6X2pIQ4u8APARAQb2bWXmBrxHRCRxterq5ZNQLi8U4d+YLhQJisZhm9EAqlcLIiDGf0jZjriM6PdFMCf/5wrR6vGX58Bn/TCklcrkcotFoS1OgkZERjIyMcPnsaWKuo0EjpcQzB1PYHcqiomiX0W7xCxw7dkxzbmRkBH6/nzmmg9rpUvt2AN8A8Abqd8JWCyE+LqW8T+/giPrRkVBj/+ZSg+zfLJVKiMViyDctNQHqF3/9kpCZ64hOz2e/v0N9PT5sx1XnBM/o51UqFUQikZZ843Q6EQwG+2kZf1cw19GgmU6V8ErTHnMAMAuJLcMKbOXGebPZjPHxcY5T0kG7XWqvkVLuAwAhxFkAfgKAiYnoNEyHmvZvjvf2k8FKpYJ4PI5MRpuohRDwer3w+/39tHeKuY7oFL1yOKk5/rWLlsFmOb3ltFJKJJNJxONxyKZmHmazGaOjoxgaGuqbG1xdxlxHA0NKiWcPafPUhMuE1fYi3JZGnnE6nRgfH4fFov/84EHUzn/V8FxSmrUfQFineIj6XjSZU1+Pj/bm/s1arYZEIoFUKqW58APqTTr8fn8/7mtgriM6RS8eaFzI+VxWbFt5eqs2isUiwuEwymXtyk6v14tAINBPN7Z6AXMdDYRyTcFjb8QRzc2ObJISV0xaYa/mNJ/z+/1cpq+zdgrOnUKInwL4AQAJ4FYAvxRC3AIAUsr/0DE+or6SyhSQyjSWiTkdvbU0TFEUJJNJJJNJzdgBAHC5XAgEArDb7V2KTnfMdURtKlcV7DySwpN7o+q52y5becoXbLVaDbFYDOl0WnPeZrNhbGwMDoejI/GSBnMd9T0pJe58bhpzt8wVRYHXVIGtUlLHnVgsFoyPj7P52CJop+B0AAgBuGr2OALAD+Am1BMVExPRAhRFwf/5+k/xyt4jmvN2W28s3ZBSIp1OIx6Pa7q0AfVObYFAYBASMnMd0QIyxQp+9Nw0nj8QR7GivSkV9LR/M0pKiWw2i2g0qsk5Qgj4/X74fD4+bdAPcx31vR/vjKjFZrVahblWxgWTJjWvuN1ujI2NcfXEImmnS+2Hjz8nhLCxoxlR+/ZOhVuKTQBYEjzzbo5nYu6iLx6Po1KpaN6zWq0IBAJwu90DceHHXEd0csVyDf//fa/jUCzf8t66iSFMjrT3NLJSqSAcDqNQKGjOu1wuBIPBflyu31OY66jf7TiWwUymBCklyuUyqtUq3rHCDLOp3ugwEAhgeHh4IK5tekU7XWofBfAhKeXU7PFFAL4FYKuukRH1kXyx8e+402HDOavHccUF67B0rHtdaudmaR4/SN1iscDv98Pj8QxUMmauIzqxak3B1x56Q1NsjnvtuHCNH5uXebFmbOGGPlJKJBIJJBKJlqZAwWBwYG5udRtzHfWzN6J5PDVV3xZUKpWgKAquW1ovNq1WKyYmJvp5a1DPamc9358D+JkQ4qsAlgL4FQAtd8eI6MSUpourDWsm8L8+/itdi6VYLCIWi7U8XTCZTBgZGcHw8DBMps4MbTcY5jqiE/jFG3Hsmm7ss7z14mW4cct42wVioVBAOBxuWUkxPDyMQCAwqDmnW5jrqC8lCxU8vC+GSqWiNiC7eMyEIauAx+NBMBhkrumSdpbU/lwI8d8BPAAgCmCblHJG98iI+ojSNGjY3KVkVy6XEY/Hkc1mNeeFEPD5fPD5fAO9l4G5jmh+T+2N4s7Hp9Tjy9YH8JZzJ9r6bq1WQzQabRmtZLfbEQwG2RSoC5jrqB9Vagr+9aVj6hJaIYDzAiZMuusrKAZt1VavaWdJ7ecAvBvAlQDOBfCoEOL3pJQ/0Ts4on5x/1M71dcm0+ImvGq1ing83tIFEoA6S5Nzp5jriOaTL1Vx15MHNefedFZgwe9JKZHJZBCNRjUdr00mE/x+P/dPdRFzHfWj+3aFUCgU1OX6FwdNWOFzYGJiAjZbb00EGETtXGWOArhYSlkA8IwQ4meor/VnYiJqw3M7pvDS7sPqsdu5OHsHarWaOuLk+FmabrcbgUCASViLuY7oOKF0CdWmFRqXrx/FhknPSb9TLpcRiURalu273W4Eg0He4Oo+5jrqG1JKbD8YxuuhlOb8+gkfRkdHuYS2R7SzpPZ3AUAI4ZZS5qSUBwHcoHtkRH3ikV+8pr72uB245YZtuv55iqIglUohkUi0zNJ0Op0IBAJcxjYP5joirVKlhh/8onGzbONSLz505aoTfl5RFCQSiZabXBaLRW0KRN3HXEf9olarYWZmBg/tayzZF0LgYxdPwuM5+Y0xWlwLlv1CiEuEELsA7J493iqE+JrukRH1gXKliu17ptXjL/yPm3QbhTI3S/PQoUOIxWKaYtNms2HJkiWYnJxksXkCzHVEDdWagi//1x68PtPY873Mf+JZvPl8HocPH27pQOvz+bBixQoWmz2EuY76QT6fx8GDB3H33kaxaTKZ8LaNEyw2e1A761q+AuAtAO4BACnldiHElbpGRWRwlUoNT764D/c/vQulcr0r45LgMFZOLrz36VRJKdURJ3Nd2eZYLBYEAgEMDS08soCY64jmfO/pQ5oRKCsCLly/abzlc9VqFdFotKUZmcPhQDAY5PiB3sRcR4YlpUQ8Hkc8HsfLMQWlWv281WqFzWrFhiXdnW9O82trI4WU8vBxF6s1fcIh6g9/def9eH6nttHGm89d3fE/p1AoIBaLoVgsas6bzWZ1xAkLzfYx19GgK1VruOvJg3h2X1w9t22VD5+49ixNw7O5FRXHr6YwmUwIBALwer3MPT2MuY6MqFqtIhQKIZvL4+mQgnhJQggBu80Gs8WC285f0u0Q6QTaKTgPCyEuBSCFEDYAn8LsMgwiapXOFlqKzU1rJ3FzB/dulkolxGIx5PN5zXkhBEZGRuDz+bhR/tQx19FAi2RK+OrPX8exZOMGlt1qwoevWKUpNkulEiKRSMuNLo/Hg0AgwKZAvY+5jgwnl8shFApBURQ8G64Xm2azGXa7HV6HBbdsGYfTOrij3XpdO/8q/HcAf4P6cOAjAO4H8Nt6BkVkZF/61s81x1/5o/dg2bivI3f7K5UK4vF4y0w7IYQ64mSQZ2meIeY6GlhSSvzt/dpic5nfiQ9evhIue/1SQVEUxONxJJNJzXetViuCwSBcLteixkynjbmODENKiVgshmQyiXJN4uGjNZRqjSW0y0eceMvZo7As8sg5OjXtdKmNAnj/IsRCZHivHwxhz4HG/OybrzsPyydGzvjn1mo1JBIJpFKplhEnHo8Hfr8fVqv1jP+cQcZcR4PsWLKIo4lGsfneS5bj2o1j6o2yXC6HSCSCarWqfkYIAZ/Ph5GREa6oMBDmOjKKSqWCmZkZlEr18Uz3Ha5BCAGHww6z2QyX1Yy3nTMKE5fv9zyueyHqoHsf3aG+vmjzKtz2q28+o5+nKIo6S/P4ESculwuBQIBNOYjojP10+zH19dIRJ66bbRBUrVYRiUSQy+U0n3c6nQgGg5zlS0S6yGQyiEQiqNVqOJqXeD6iqEtohRAYsplxy5ZxFpsGwYKTqENe2XMET724Tz2+4sJ1p/2z5hpyxONx1GraXg4OhwOBQABO54lHFBARtSNbrOKOR/Zj13RaPXfF2aOQUiKVSiEWi2lWVZjNZgQCAXg8HjYFIqKOUxQF0WgU6XQa4YLEC5Eaykp9vJvVYgFm8857zpuA1cyVFUbBgpOoQ+5/utFzIeBz4+LNq075Z0gpkc1mEY/HUalUNO9ZrVYEAgG43W5e6BFRR/zBv25HpdYoKM9dPoxL13hx5MgRlEolzWe9Xi8CgQD3iRORLsrlMmZmZlAul7EvpWBnQoGpaQktAHjtFty6dZzFpsGcsOAUQnzmZF+UUt7e+XCIjOtYJKW+/uA7L4H1FLulzc3SPP4iz2KxwO/384mCTpjraBBJKfFvzx7WFJv+IStu3uLF0aPTms/abDYEg0GuqjA45jrqVXOruqLRKKSUmMrUi02LxQKbzQaTEFg76sKGcTeWeOy8FjKgkz3h9Mz+fjaAizA7IBjATQAe1zMoIqN56NndmJqOAgBMQmDjWe3PgioWi4jFYigUCprzJpNJnaXJhhy6Yq6jgSKlxJ2PT+Hp12NzZ1Ct1vBbF/lRyjc6YM+NWRoZGeEFXn9grqOeU6vVEIlEkM1mAQB7kwp2JxXY7XZYzGZACNy6dQJ+FxsjGtkJC04p5RcAQAhxP4DzpZSZ2ePPA/jhokRH1OOklHjo2dfw9X97TD136flnwT/sXvC75XIZ8XhcTbJz5jo/+nw+Ll1bBMx1NGh+/OJRtdiUUkGpVMZnrg4CstGYzOVyIRgMsvt1H2Guo15TLBYRCoXULUT7Ugr2pOtNyUwmE2xmE27ZMgafk3nI6NrZw7kCQLnpuAxglS7REBlIrabgy9/6OV7YdVA9Nx7w4sM3X3rS71WrVcTjcaTT6Zb35mZpcnB6VzDXUd97+WASP3n5GACJSqUKv0PifW8ahddRv7llNpsxOjqKoaEhPtXsX8x11FXzNSU7klWwJ2OCw2GDEAICwHu3TcB5ituTqDe1c1V7F4DnhBB3A5AAbgbwHV2jIupx5UoV/+frP8GuNxqjBBx2K/6fD14Hn2f+4ee1Wk0dcXL8LE23241AIMARA93FXEd96/kDcdz9y2mE0iXUajWUy2W4rMCH3jQGt61+QTc8PAy/38+VFf2PuY66plarIRQKIZ/Pq+em88CrGSvs9kZZcutWFpv9ZMGCU0r5Z0KI+wBcMXvqw1LKl/QNi6i33ffETk2xGRzx4E9/950YHRlq+ayiKEilUkgkEi2zNJ1OJwKBABwOh+4x08kx11G/empvFHc+PgUpJcrlMqrVKpxWEz5xeb3YtNlsGBsbYx4aEMx11C2FQgGhUAjVarVxDlbszAAWS71XhcNiwq9uGuOezT7T7ro9F4C0lPJOIURQCLFaSnlAz8CIelUsmcX3/usX6vFVF63HR265DEMuu+ZzUkpkMhnE43FNcgXqXR8DgQBcLheXrfUW5jrqK7FsCd958iCq1SrK5TKklFgTsONtG4cx7LQgEAhgeHiYeWjwMNfRopFSIpFIIB6Pa84XrUN4aroMk6mRf961mXs2+9GCBacQ4k8AXIh6V7M7AVgBfBfAZfqGRtRbpJSYmo7hi1//CWq1+pPK4IgHn/yNq2CxmDWfmxtxUi6XNT/DYqlf4HF/VO9hrqN+dNcTB5DLF1Cr1QAAb90wjMvWDMHtdmN0dJRNgQYQcx0tpmq1ilAopOnEbzKZYB8O4MG9aaDpWuicMTeLzT7VzhPOmwFsA/AiAEgpjwohPCf/ClF/KRTLuO0P/6nl/PvecZGm2CwUCojFYigWi5rPmc1mdcQJC82exVxHfUNKiTsf3oPnXg9hbsv4+y7wY8syj9oUiAYWcx0tilwuh3A4rN7wAupbiSweP+7eGVXPmQRwzVo/1o0u3OGfjKmdgrMspZRCCAkAQgj+v4EGzv1P72459963X4wrL1wPACiVSojFYppN8EBjjp3P5+Mszd7HXEd9IZ/PY8/UMTzwakg9F3Bb8KazJzAaCDAXEXMd6UpKiVgshmQyqZ6rKRJZiwc7EwLHDkU1n79uXQBnBeZvuEj9oZ2C8wdCiG8C8AkhPgbgIwC+pW9YRL0jHM/gp4/v0Jz7yC2X4Veu3IxKpYJ4PI5MJqN5Xwihjjhhx0fDYK4jQ6vVaohGo0gk0/irh46q500mE37/ps0YCw53MTrqIcx1pJtKpYKZmRmUSiUAQFWR2JsGDhetMJsrLZ9fNeJksTkA2ulS+1dCiBsApFFf7//HUsoHdI+MqEd84gvfU1+bzSZ864sfgNtpQywWQyqVahlx4vF44Pf7uTfKYJjryKjmGpRFo1EoioJ/eSEGRalvjbLZbHjfZauxapzFJtUx15FestkswuGw2pE/UZL4RVTAbLXBbNZuJ1o14sSWJUOY9Nrn+1HUZ9ppGvRlKeUfAnhgnnNEfe3v/+VRzfGtN56ParmAg+FjLSNOXC4XAoEA7HYmTyNiriMjKpfLCIfD6r7xbKmG1yMlWCz1cSfDLhtu2Dze5SiplzDXUacpioJoNIp0Oq2eO5RVsDNtgdVq0TQGmvTace1aP4bs7Q7KoH7QzkaOG+Y597ZOB0LUa+KpHB7+xWsAACnry0QuPDuAeDyuKTYdDgeWLl2KyclJFpvGxlxHhqEoCmKxGA4dOqRpUnbnc3E4HHbY7Q4IYcKfv2cLG5XR8ZjrqGPK5TKOHDmiKTZnigK7s7b6Si8hYDEJbJkYwnvOm8CvbhpjsTmATvi/uBDiEwA+CWCNEOKVprc8AJ7SOzCibvvHHz0FKYFarYpyuYLP3HaZptOa1WpFIBCA2+3mBZ2BMdeR0eRyOUQikZb5vq8nTchWLerStVsvXga7hXvIqY65jjppbil/JBLRbC0qmp3Yka5pltDetDGIcQ9vyA+yk91i+BcA9wH4cwCfbTqfkVLG5/8KUX/I5Ip46sXXUS6XoSgKbrxkHVYv9QOoz9L0+/3weDwsNPsDcx0ZQrVaRTQaRTab1ZyfyQGPHSjhQLSg5qTAkA2Xrg90I0zqXcx11BGKoiAcDmtyUbIMTJXsiBZqmmujd20eY7FJJy44pZQpACkA7wUAIcQYAAeAISHEkJTy0OKESLS48vk8/tftP9IsU7vmwrNgMpnUWZocK9A/mOuo10kpkU6nEYvFNMv5S1XgRztzOJQoA9De/Pr0W9fD42DjMmpgrqNOKBaLCIVCqFTqHWdDBYk3MgJZaYXJBM1+zevXBTDBYpPQXtOgmwDcDmASQBjASgC7AWzSNzSixVUul/HyzjfwpX98EPliWT1/01UbsGLZBHw+H0ec9DHmOupFpVIJ4XBYHTEwJ6vY8LdPhGafJGiLzc/edA4mfI5FjJKMhLmOToeUEqlUCrFYTF1CGytKPB8TsNlsMJkaecjntOCCZV6sHeW4E6prZ9funwJ4M4AHpZTbhBDXYPbuGFE/qFariMfjeHnXFG7/7hOa9666cB0+/t4bYbFwg/sAYK6jnqEoCuLxuGZwOlDfO+7wjOBL/7FXs2zNaTPj3W9ahsvXj3KpPy2EuY5OSa1WQzgcRi6XU88lSsAvExbYmxoArfE7cf4yL0bdtm6EST2snavoipQyJoQwCSFMUspHhBBf1j0yIp3VajUkk0kkk0ns3h/C333/GfU9s9mMc89Zgf/xARabA4S5jnrCfE2BhBAYGRmBa8iLr/x8n+bzJgF89QPnsdCkdjHXUdsKhQJCoZCaj6SUiFSs2J4SsFga24vOXTKES1eNdCtM6nHtXEknhRBDAB4H8D0hRBhAdYHvEPUsRVGQTqfV8SaPPr8fP350FwDAZDLDZrPiuks24nfef02XI6VFxlxHXVWtVhGJRDRPEQDA6XTCHxjFM/tT+M8XdiBfanTLvmZjEO+/dOVih0rGxlxHC5JSIpFIIB5v9JOayig4VLCgDJPmBtfZQTeLTTqpdgrOdwIoAvg0gPcDGAbwRT2DItLDXAvveDyu3ql7Yfc0/v3BHTCZTLDbHTCbzfjsx96Ki7es6m6w1A3MddQV8+2NAuorLUZHRwGLA7/z3e0t37tqA4tNOi3MdXRS1WoVoVAIhUIBAFCoSrwQlchJK8xNq75MArhubQBnca8mLWDBglNK2Xyr9ds6xkKkCykl8vk8YrEYyuVGM6DpcAr/fM8LsNvtMJstEAL47Mfeios2r+pesNQ1zHXUDcViEZFIpKUpkNfrRSAQgNlsxh0P72/53q0XL8ONW8YXK0zqI8x1dDL5fB6hUEidO54qSzwRkvWb8k1PNc9dMoRtS71wWtlMkRZ2woJTCJEBIJtPzR4LAFJK6dU5NqIzVigUEIvFNCNOAGDvoRi+8e/Pwel0qR28/+GLH4B/2N2FKKmbmOuoG2q1GuLxOFKplOa8zWZDMBiE0+mElBLfeXIKz+3Xjki8/f1b4XVy5AmdGuY6OhkpJWKxmNqoTJESL0QVRMoWOOxWzbiTd2+dgN/FHETtO9kcTs9iBkLUSaVSCfF4vGUvVDSZw/2/OICX9xyD1dpIlr9y5WYWmwOKuY4Wk5QS2WwW0WhUfYIA1JsC+f1++Hw+CCGQL1XxtYfewGtHM+pnlvgc+OKvbWJzIDotzHV0IpVKBaFQSL05L6XEUyGJPOyw2RpPMNeNunDtWj9zEJ2yttpvCiEuB7BOSnmnEGIUgEdKeUDf0IhOXaVSQTweRyaT0ZwXQsDlHsKf3PEYiqWKmiztNit+7cZtuOX6bd0Il3oMcx3pqVKpIBKJIJ/Pa867XC4Eg0H1JpiiSHzh7l2IZRtbACwmgT98xzm80KOOYK6jOdlsFuFwGIqiQEqJZBl4NWVC0WRVl9CaBHDt2gDOCjiZg+i0LFhwCiH+BMCFAM4GcCcAG4DvArhM39CI2ler1ZBIJJBKpTRNNwDA4/EAZjv+8s4HUSxV1PMBnxt/9rvvQtDPm77EXEf6mev2mEgkWpoCBYNBuN1u9SKuXFVw+317NcWmf8iG//3ODRhycEQTnTnmOgLqHftjsZi6rD9alNgeU1AWVlgtFjUnCQC/eeFS2JtGoBCdqnb+9boZwDYALwKAlPKoEIJX6NQTFEVRZ2kqiqJ5z+VyIRAIoFRR8Nnb70YollbfW7HEj7/4vV+DlZvdqYG5jjquUCggEoloGpYBwPDwMPx+P8zmRg4qVWr44t27EEo3Ggi5bGZ8+T1b+FSBOom5bsCVy2XMzMygXC6jJiVejCg4VgDsdjusTTnJahb40IVLYTYx/9CZaafgLEsppRBCAoAQghvdqOuklOoszeZ9UADgcDgQCAQAYcZzOw7ie//1HCKJxhLbZeMjLDZpPsx11DG1Wg2xWAzpdFpz3m63IxgMwuFwaM7vmk7jqz9/HVWl8QQ06LHj87dsZLFJncZcN8DS6TQikUj9Oqos8XJMQbpqgtNpV3PN2oALq/1OrPI7WWxSR7RTcP5ACPFNAD4hxMcAfATAP+gbFtH85hpuxONxVCoVzXtWqxWBQAButxuvvn4Un//7e1u+f+76ZfjjT76dF3A0H+Y6OmNz835jsVhLU6BAIIDh4WFN/knmyvju04fw8sGk5ue8ea0fH7piFSxmLmOjjmOuG0CKoiASiSCTyUBKiV0JiX1pBTabDQ67Re1Ce+P6ANYEOFeTOqudOZx/JYS4AUAa9fX+fyylfED3yIiOMzdL8/h5dRaLBX6/Hx6PB1PTMXzpHx/C7v3HNJ+x26z43Q9cizedu3oxQyYDYa6jM1UulxGJRNRh6XPcbjeCwSAsTQPTS9UavnzvHhyK5Y//MbjlwqV429YJ3hgjXTDXDZ5SqYSZmRn1Rv2+tMT+jITT6YTJVL+pdd6kBxcs88LKm1ykg5MWnEIIM4CfSymvB8BkRF1RLBYRi8VaLuJMJhNGRkYwPDwMk8mEHz+8Hd/58TMt3185GcD//OhbMDHKEWM0P+Y6OhOKoiCRSCCZTGqaAlksFrUp0Jzd02n88kAcj78Wbfk5HocFv3PjWqwZG1qUuGnwMNcNFiklUqkUYrFYfYVYpb6ENlU1w+G0qTe1Llk5jK2TvEYi/Zy04JRS1oQQeSHEsJQydbLPEnVauVxGPB5HNpvVnBdCwOfzwefzqQ03fvLYjpZi0+204w//21uwae3kosVMxsRcR6crn88jEom0LPH3+Xzw+/3q04NjyQI+9+87T/hz3nfpClyzIcinmqQr5rrBUavVEA6HkcvlUFUkQgWJl2MSZqsNdnvj8v+DF0zCZWNPC9JXO3s4iwB2CCEeAJCbOyml/JRuUdFAq1ariMfjLc02AMDr9cLv96tL06bDSfz9vzyKPQdmNJ/7yC2X4Veu3MyLNzoVzHXUtmq1ilgs1jLz1+FwIBgMwm63o1pT8NiuMJ7YE5136eyY146tK3x41wWTsLOJGS0e5ro+VygUEAqFkCpU8MuIglRZwmQywW53qDfBPHYz3nZOkMUmLYp2Cs6fzP4i0lWtVlNHnBw/S9PtdiMQCMBms6nn/vOhl3HXPc+2/Jw///TNWL9qXPd4qe8w19GC5jpkx2IxzSgmk8mEQCAAr9eLTLGKp3eF8cCrIYTTpXl/zqffug4bl3p5U4y6gbmuT0kpkUwmMR2K4o20xP6MAkUCVosFVlt9Ca3NbMKVa0ZwVsDJ/EOLpp09nDdIKW9bpHhoACmKoo44OX6WptPpRCAQ0IwQeP1gCPc9sROP/XJvy8/68M2XstikU8ZcR+0olUqIRCIoFoua80NDQwgEAtg9k8NXf/jCCb+/IuDCZesDuHbjGC/0qCuY6/pXtVpFKBRCNJ3Hg9P1DtlCCNjtNnVV2LpRF960YhhD9naeNxF1Tjt7OINCCJuUsnyyzxKdqrnxAfF4HNVqVfOezWZDIBCAy+VSL8ziqRz+4YdP4LkdU5rPWixmnL9hOT74zkuwJDi8WOFTH2Guo5NRFAXxeBzJpHZ0idVqRTAYBMw2/MVPX8eBSK7luy6bGRef5cfbtk4gMGRfrJCJ5sVc15/y+TxCoRAiuSqeCdWLzfoSWjvcdgsuXzWCNXyiSV3Uzi2OKeF8kG4AACAASURBVABPCSHugXat/+16BUX9TUqpjjgpl7X/3lksFgQCAQwNDamJUVEU/NN/PI37nni15WctGx/BH/3W29iBljphCsx1dJxcLodIJKK5KTbXuGx42Ic7Hj2AF6eS8373N968HJevH4WDe6Sot0yBua4vSCkRj8eRSCQwlVGwPVZfJWa1WmGzWrF5iQeXrPTBbGKhSd3VTsF5dPaXCYBH33Co3xUKBcRisZYlaWazWR1x0nwH7lgkhb+68wFMTWtHCCxf4sd73noh3rx1Ne/YUacw15GqWq0iEokgl9M+tXQ6nfD6/Hhodxz/9fJLLd87d/kwbjp/EquD7pb3iHoEc10fqFQqCIVCSGQL2J1QcDgnZ5fQ2mE2m3HtWj/WMw9Rj1iw4JRSfgEAhBCe+qHMLvAVohalUgnxeLzl4k0IgZGREfh8PrVzGlC/a3fvo6/grnt+0bKv87ab3oR3XXceC03qKOY6Ahpz647fU24ymSAcXuyOV3Hvw68hV6q1fPe6TWN47yUrFjNcolPGXGd8qXQGew6HsD9dw3Su3mTRbDbDbrdDCIHr1wWwdtTV5SiJGhYsOIUQmwHcBcA/exwF8EEp5YkHihHNqlQqiMfjLaMDhBDqiJO5WZpzpJT4/N/fi1dfP6qeM5lMuPZNZ+Oma87FsvGRRYmdBgtzHRWLRUQiEZRK2s6yisWJu3dmsOfY1LzfW+Z34o9uOoejTcgQmOuMq1yt4eHdR7EnkkO16V68zWaD1WLB6oALl68egZvL+KnHtLOk9g4An5FSPgIAQoirAfwDgEt1jIsMrlarIZFIIJVKtYw48Xg88Pv9sFqtx31HwU8ffxX3ProdsWTjSejEqBef/uD1WLtybFFip4HFXDegFEVBLBZDKpXSnJfCjF1xEx5+LdzyRNNiEmozoCU+52KGS3SmmOsMJlmo4PlDCeyYTmpWXswtobVbLbhizQjWj7q4+ot6UjsFp3suKQGAlPJRIQQXhdO8FEVRZ2kevxTW5XIhEAjAbtd2apRSYs+BEP7pP57CG4cjmvcEgL/8/V+Hy2kDkc6Y6waMlBK5XA7RaFTTFEgCOJix4J4dCeTL2kJz41IvtiwfxgWrRuAfYl4iQ2KuMwhFShyIF3DfrlDLygunzYKzJ3zwu23YOD4Eu8V0gp9C1H3tFJz7hRCfQ335BQDcBuCAfiGREc0NQ4/H46jVtBdoDocDgUAATqdT8/kde6dxzyPbsX3PdEtxCgBXX3w2PvSuS1hs0mJhrhsglUoFkUgE+XweAFCuKtgTLiJWFHjmYAFCaC/eHFYTPnzlalywmkv6yfCY63pcqarglWMZ7DiWQSZfbBkdt2nCgxs3LtH0viD6v+3deZAkWX0f8O8vM+u+KyuremaPmdmLvVn24DCwrEFeLGwBYZAgjGWQHYFx2FIYWcE/coSMT8kK4wgfipAsARaWwRwGAxZiEccu7LK7Ys9Z2F32mL1mu6urKru66z4yn/+orJrOrp6Znpmuruv7iajoqqyq7Fc10794v5fvvd8s20vC+Q8AfBLA//Ee3wPg1ybWIporSinU63XYto1er+d7LhAIwDRNxGIx3xSPp0+s4ff+5NvYrLXGzqfrGt56y5V4/503s6YmHTTGuiWglEK1WoVt24MrnF0HP3imhgdebCIYDMIw9LFk8723HMbbr80jymLptBgY62bYyc02vvGzElzXRafdhrttWVIypOO9rz0MK8kL0jRf9rJL7QaA3ziAttCcGdbS3DnNwzAMZLNZJBIJiAiUUnjx1QqO//wkPvPV+057vjfceAy//M5bcOzi3KSbTjSGsW7xtdttrK+vo9vtYqvt4J5na3j4lSaU6IhE/EXRg4aGy/MxvOumQ7jmMOv80uJgrJtNnb6L1a0O/uKpEnr9vq9OeSEiuDofw02XHYKhc0Mgmj972aX2OwB+WSlV9R5nAHxBKfXOSTeOZlO73UalUkGr5b9CqWnaqJampmlwXRdPPPMqPvf1+8fWZg4Zho4P/uKtuPPN1yIWCe36GqKDwFi3uBzHQaVSwUZ1E4+80sTx1RZesDsANIRCIWjaoAMX0AVvuNzEaw4lcMuxDIJcE0ULiLFutiil8D8fXkWj60AphU6nM1qadDQhuDaj46KV/GgQn2ge7WV+UG4YlIDByJiIcLvQJdTtdmHbNup1f8kuEUEqlUImk4Gu66hU6/jc1x/AfY8+B8cZX5sJAFdcmsfHPnA7r2bSLGGsWzDDKf+PPvsq7n1uEz9ba6PnKIgAgUAQgYABQLCSDuPdrzuMm4+mYehMMmnhMdbNgFbPwVa7jx+e2ECj68BxHHQ6ndHO/tdnNVyTC2NlZQXBIPeyoPm2l4TTFZFLlVIvAYCIHMFgEz9aEv1+H7ZtY2tra+y5YS1NwzDw0qqNz371Pjz+9Cu7/ge59vJDuO2Go7j62AquOlqYfMOJzg1j3QJZ22jgS/c+i/ueq/qOG4aOYDAIEQ0XZyP4pdcdxk1H0tA1XjmgpcFYNyWuUnhitY7jazXUhqWWlPJNob0oJjgcFVxzOAPTNLkxEC2EvSScvw3gRyJyt/f4dgAfnVyTaFY4jjMqcbKzlmYsFoNpmuj0XHzvgZ/j+DMncd8jz+16nne88Wq86/brcfQiXs2kmcZYN+daXQfffnwV9z61hpN2A9vDloggGAwiHgni1mNZ3HGNhaMWN96gpcRYd8BcpVBp9PCXz1Sw2d5WgmnbFNrLkxquzQgMXUc+n0c8Hp9ii4n21142DfoLEbkZwBsxKIv4caVUeeIto6lxXXdU4mRnuZJIJIJkKo17Hnoef/njH+KlVXvXc1x/5WG8/Q1X4/U3HEUkzKkgNPsY6+bXYy9V8Sc/OIF2r49GswXX9Q+QBQIGjuRTeN9tF+Pai5Jcm0lLjbHuYD1XbuJHL2yg1fP3pxzHgfQ7sELA0YSOQkQQDodRKBQQCASm1FqiydjTHu9eIPrmhNtCU6aUQq1Wg23bYzWfAoEAOo6BB59cx9e+exfqzc6u58gko/jwe96Et9565UE0mWhfMdbNB6UUWl0HD79YxbcfX8OrGy10u92xuHUsF8FtV63gtstzuDgbnVJriWYPY93BeHK9jruf2/AfVAq6cnBrpo906NSOs+l0GqZpcmMgWkgsKkZQSo1KnGzfhhsAHBc4/ryN7z34LIqV8TWcQ++6/Xq87darcPmlFoMlEU3Ez9dqeOSFKh59sYpSrQNAoe+tfdo+ffad16TwtusvwtFDOcYjIto3Sin0XIWeo9BzXPQcha7jou8d63rHeo4Lu9nD87Z/N/8j6RAyaME0+qPYpHtTaGMxTvGnxXXahFNEjimlThxkY+jgtVotVCoVtNvt0bFur4/Hnyni8WdLeP7kBnp9Z+x94VAAb73lClxz2SG89ZYruKid5hZj3ex7xW7i3/zfJ9F3TmWVruui2+2OygdcuxLGG47EccORLCzLgmFwPJVoO8a68+O4Cve/WMWzlebYtNhzcceRGILtqrdUaZBsRiIRFAoFxitaeGf6H/5lALeIyHeVUu84qAbRweh0OrBtG41GA51uHy+tVfH8SRv3PfYSthpdBAKBsSsD0XAQ1195GK+/4RjedNNlCIe4xoAWAmPdjGp0+vjEFx5HZ1snTymFXq+Hfr8HK27gaDaGmy+O4kguCsuyeJWA6PQY685BrdPHgy9t4ply84LOY8UCuCTiwmja2J6uZrNZZDIZzsKgpXCmhFMTkd8BcJWI/ObOJ5VSn5pcs2hSer3eqMTJ//vR03jimTWslmtwXBeGEUAwGBir9xQKBvChv/16vOONVzPJpEXEWDcjyrUO/vyxVdz/rI2ALmh0/LMrHMdBt9vBu69P4YbDEQS9mpmZTAaZTIYzLYjOjLHuDJRSOL5Wx+pWB52+i7VaB+4uxWICmsDQBQFdQ1AXBDQNAV282+CYoWkIGYJ81EC/VkGnc2rfC8MwUCgUEIlEDvDTEU3XmRLODwJ4r/eaxME0hybFcRyUyxXc81dP4akXSnj856uoeRv/GIaBSCg01ll755uvw9WXFfCGG48hFGSiSQuLse6A9B0XW60+qs0uNps91Dt9tLoOKvUuHjqxgWqzN3ptd9v+P0oNps+++7okrj+URUAfXBEIh8OwLAuhUOigPwrRPGKs26HW6eNHJzaw1e5jo9U/7euCuoabLkrgpsMJaHu8Ilmr1VAqrfl2+4/FYsjn89B1/QzvJFo8p004lVJPA/g9EXlcKfWtA2wT7QOlFF4tbeLJ51bx6M9O4KfPnsRqyb/pj67rCASC0HUNh60Urr7sEK48kseNr7kYK7nklFpOdLAY6/af6yqU6x1stfo4abew1e7hh0+XUW10d71icHoK2YiOXBh4zw0F6Nqgo6dpGkzTRDKZ5HQ0oj1irPNb3erge89WUOuM71MxVIgH8cYjaawkgnuONa7rolwuY2vrVJ9LRGCaJlKpFGMWLaW9rFK+T0Q+hUFhYAC4G8C/UkptTq5ZdD7szQaef6WM518u4XsPPI1XizZ6vR6U8vfwNE1DMBhEKBTEm157Gd535824ZCUzpVYTzQzGuj2ot/t4tlhHt++i1u7hRKmBWquPWruPTt9Bp+dis9WDOqfE0u/mo2nceV0OoX7NNxUNABKJBHK5HK8QEJ2/hYp1tU4f6/XuYLdYx9tB1h3uFqvQd110HTV4btvxZm/3RDNkaHjbZRmkIwFkIsY5JYidTgfFYtG3438gEEChUEA4HL7gz0o0r/aScH4awBMAfsV7/KsAPgPg70yqUbS7ft9BZbOBjc0mVkubePL5VbxSrGK9soXqVhMKgFKA4/TR7faglH83NREN+VwK1195Ed588xW49bojCAa4MxqRZ6FjnVIKjjvodA227nfR63udsf6prfyHz5drHaxvdtDsDpLJrVYPG40euv3z36Vx6FIzinQ0gHjYQDSoIxY2cCgdxqF0BCvJIDY2NlCtlrE91QwEArAsC9Eo62kSXaC5jnVKKazXu3hxo40XNlqwt03FPx+aADceSuCGQwmEDA2Gdu5XIJVS2NraQrlc9g3yx+Nx5PN5ri+npbeXbONypdT7tj3+pIg8OqkGLSPXddFs97Cx1cSLr1ZQqTZgVxuobDZgbzawWWui3uyg2erCPcNlg8GGGl3feoGrj+Zx9bE8XnfdMdx49VFEwsHTvp9oyU0s1jU6fbxit7C+1Ua5Nli/qKDgqkFHRSnA3fFTYTA11VVqNJg0ek5tey8Gx4d/9q5SY+dylUK10UP/3OazXpBYSIeVDCEZDiAa0nFlIYFrLkognzz9KH+j0cDLL7+Mfv/UWioRQTqd5qZARPtnrvp1Sil0+i6K9S5esFt4caN92quT50IT4HIzitsuSSEZPv/Bd8dxUCqVUK/XR8dEBJZlIZFIcAotEfaWcLZE5C1KqR8BgIi8GUDrLO9ZOkopuK5C33HQd1z0+y5qzTY2NpvYrLWwsdXEZq2JcrWB8kYdW/UWmu0umu0eOt0LG50bJJo96Bpw7HAGeTOOfCaGW6+7BFccvQipVIodNaKzm1ise+ylKj599wv7caqpEwHCAR3JiIHL83EEDQ3ZeBDXHE4iHNAQMnQkIgYC+t5jTr/fR6lUQqPR8B2PRCKwLGts52wiuiBz0a/rOi6+/tN1bLUddJ3Tz6zQRXAoGUQsaCCgCwxNENQ1byfZHbvIju5r5301c7t2u41isYhe71Q/LhgMYmVlhXGLaJu9JJwfA/CnIpLyHm8A+PDkmnTuhsme8kb2XVedujKgTt13XXc02u84LlrtLnp9B447eDw87rguXFcNfjpq9Ljb62OtvIWNrSZqjTbqzQ4q1TpqzQ6cvoODuHaQSUaRTcWQy8SRS8dwKBtGOh5AOh6GYWgQEYgIUqkUMpkM1zkR7d3EYt2ZruodJH3bdv4BfdApCxjatmOnOmMBQ0PQ0GDGgjiWjyEZCSARNhAPGdAusJM2pJTC5uYmKpWKbxqaruswTZNXB4gmY+b7dcCg/Mhmq4/eLjMzwoaGI5kIjmTCuCQdPqcBrv2glEK1WkWlUvEdTyaTyOVyHOQn2uGsCadS6jEArxWRpPd46yxvuSDff+BpfP7PH9yWJO5MGk8llso7tgjCoQBikSAuPZTFSi6FbCoGMx1DNhVDJhVFIhpGLBKEYejo9/vY2NjA5ub4+v5kMolsNgvD4NpMonMxyViXT4ZwzIrBSoRgJUPIxoLQNEATgSYCEYx+igACga4JBABk+Dp4A0rwvWeY+2ki0DTvdRg/ZzxkIBqanbjQbrdRKpXGNgVKJpMwTZODZUQTctD9uvMlIkiEDdjNHgxNkI4YuDgVxtFMBPlEcM/lSfab4zgoFotoNpujY5qmIZ/PIx6PT6VNRLNuz72PgwpI7W4PlWrj7C+cQQLAMHTougZD1xCLhJBORpHxbsl4GGY6BiuTQCoRRTQcQDQSRDS8t+22HcdBpVJBtVod23k2FovBNE1O4SC6QJOIdclIAL/9nmv2+7RzyXEc2LY9NmAWDAZhWRaLoRMdkFlNNLf7G1eZCOkaIgFtJmY7tFotrK2twXFOrSENhUJYWVlBIMB65USnMzvD3Z7zHbESAJo+CEiaN61U1wY/NW048j/4OXyNoWuIhIMIBHRoItB1Dbo2uGma935Ng67L6FguE0chm0QyHkYoaCCdjMLKxBEw9IlNoXBdF1tbW7Bt27chEDBY42SaJrfbJqKZppRCo9FAqVTyddZEBNlsFul0eiY6lEQ0OzKR2UjilFLY2NiAbdu+4+l0GqZpMnYRncXMJZy333olbrnuyGA6mKaNJYnD5FGw7f6C/qErpVCr1WDbtm/XRmBwNcA0TUSj0YX9/ES0GHq9Hkqlkm8KGgBEo1FYlsUrA0Q0s/r9PorFIlqtU/sqaZqGQqGAWCw2xZYRzY+zJpwiogP4WwCObn+9UupTk2hQJBxc+tIdSik0m01UKhVf8WAAMAwDpmkiHo8z0STaRwcd65bBcGMN27bHNgWyLAuxWIxxjOiAMdbtXaPRwPr6um9WRiQSQaFQ4F4ZROdgL38t3wDQBnAcwIVX/KYzarVaqFQqaLfbvuO6riOTySCVSrGDRjQZjHX7qNVqoVQqjQ2apVIpZLNZbgpEND2MdWehlBrtmbFdNptFJpNhP4zoHO0l4bxYKXXjxFuy5DqdDmzbHqtDJyLIZDJIp9PcZptoshjr9sFwc7OtLf9+JKFQCJZlcb050fQx1p1Br9fD2tqabwdtXdexsrLCTc2IztNeEs5vicidSqm7Jt6aJdTr9WDbNmq1mu+4iIxKnPBKANGBYKy7AEop1Ot1lMvlsU2BTNPk7Ayi2cFYdxq1Wg2lUsm3QWM0GkWhUGBfjOgC7CXhvB/AV0VEA9DDYENYpZRKTrRlC85xnFEtzZ0lThKJBLLZLDfSIDpYjHXnqdvtolQq+TbVAAblmnK5HGMZ0WxhrNvBdV2Uy2XfzAwOlhHtn70knP8RwJsAHFc7MyM6Z67rolqtolqtjpU4iUajME0ToVBoSq0jWmqMdedoWCpgY2PDN3BmGMZoUyAimjmMddt0u12sra351psbhoGVlRUuASDaJ3tJOJ8B8ASD0oVRSo1qaW6fbgYM1jblcjmuDSCaLsa6c9BsNlEqldDr9XzH0+k0stks15wTzS7GOpwqPVcqlXwDZvF4HJZlcQot0T7aS8K5CuAHIvItAKMV1Nw+e2+Gxc4rlcpYxywQCMA0TZYGIJoNjHV74DgOyuXy2LrzUCiEfD7PGRpEs2/pY53rulhfX0e9Xh8dExHkcjkkk0n2yYj22V4SzhPeLejdaI+GtTS373QGDHY7y2azDGpEs4Wx7gyGVwPK5bJvOYCmaTBNk/GMaH4sdaxrt9soFou+iwDBYBCFQoEDZkQTctaEUyn1yYNoyCJpt9uoVCpjG2homjaqpcnpZkSzhbHu9LrdLtbX18fqA8fjceRyORZAJ5ojyxrrlFLY3NxEpVLxTaFNJpPI5XLslxFN0Fl7CSLyfQBj8/yVUm+fSIvmWLfbhW3bvikawGCaRiqVQiaT4ZoAohnFWDfOdd3RpkDbcVMgovm1jLHOcRwUi0U0m83RMU3TYFkWEonEFFtGtBz2Miz9W9vuhwG8D0B/Ms2ZT/1+f1TiZKdhLU1eASCaeYx12zQaDZRKJfT7/q8gk8kgk8nwagDR/FqqWNdqtVAsFn2xLBQKYWVlhSWbiA7IXqbUPrTj0L0icveE2jNXHMcZlTjZudlbLBaDaZoIBpdueQTRXGKsG+j3+yiXy2MzNcLhMPL5PGMa0Zxbllg3LNtk27bveDqdhmmaXHNOdID2MqU2u+2hBuAWACsTa9EccF13VOJkZy3NSCQC0zRZu4lozix7rBuub9oZ1zRNQy6XQyKRYAeNaAEsQ6zr9/soFou+vTQ0TUOhUOBSAKIp2Ms8z4cwmOsvGEy5OAHgH06yUbNquEujbdtj08yCwSBM00Q0GmWnjGg+LW2s63Q6WF9fH9tRO5FIIJfLce050WJZ6FjXaDSwvr7uq3keDoexsrLC5U1EU7KXKbXHDqIhs0wpNSpx0u12fc8ZhgHTNBGPx5loEs2xZYx1ruvCtm1Uq1Xf8UAgAMuyEI1Gp9QyIpqURY11SilUKpWxeJbJZJDNZtlHI5qi0yacInIbgJeVUmve47+PwcLyFwH8S6WUfbr3LpJWq4VKpTJWDkDX9VGJEwYxovm1rLGuXq+jXC77ZmuIyGhTIMY1osWyyLGu1+uhWCz6+mq6rqNQKHDgjGgGnGmbwT8E0AUAEbkdwO8C+FMAmwD+aPJNm65ut4vV1VWcPHnSF8BEBNlsFkeOHEE6nWanjGj+LVWs6/V6WF1dxdrami/ZjEQiuOSSS3glgGhxLWSsq9frePnll319tWg0iksvvZTJJtGMONOUWn3baNcHAPyRUuorAL4iIo9OvmnT0ev1YNs2arWa77iIjEqccD0T0UJZilinlEK1WoVt275dtXVdRy6X47IAosW3ULHOdV2Uy2VsbW35jpumyQsCRDPmjAmniBhKqT6AdwD46B7fN5ccxxnV0txZ4iQej8M0TdZrIlpMCx/r2u021tfXx9agJ5NJmKbJQTSi5bAwsa7b7WJtbc0X0wzDwMrKCqsEEM2gMwWYzwO4W0TKAFoAfggAInIFBtMvFoLruqNamjtLnESjUZimiVAoNKXWEdEBWNhY5zgObNvG5qb/YwSDQViWhUgkMqWWEdEUzH2sG1YLKJVKvosDsVgM+Xyeg2dEM+q0CadS6t+KyHcBHAJwlzr1l60B+PWDaNwkKaVGtTS3b50NAKFQCLlcjp0xoiWwiLFOKTXaFGh7fBuuQed0M6LlM++xznVdlEol35InEUEul0MymWRMI5phZ5xCoZS6f5djP59ccyZPKYVGo4FKpYJer+d7LhAIwDRNxGIxBi6iJbJIsa7X66FUKqHZbPqOR6NRWJbFpQFES2xeY12n08Ha2pqv3xYIBLCyssJZaERzYK7m7F+oYS3NncXNdV1HNpvlCBkRzS2lFDY2NrCxsTG2KZBlWRxII6K5o5TC5uYmKpWKL64lEglYlgVNO1OxBSKaFUuRcHY6HZTLZbRaLd9xTdNGtTQZtIhoXrVaLZRKpbFNgVKpFEzTZHwjornjOA7W19fRaDRGx0QE+XweiURiii0jonO10Alnr9dDpVJBvV73HRcRpFIpZDIZLjAnornlOA7K5fJYGadQKATLsrhbIxHNpVarhWKx6KsVHAqFUCgUEAwGp9gyIjofC5lw9vv9UYmTnYa1NA1jIT86ES2B4U6NlUplbFMg0zSRSqU4fZaI5s5waYBt277jqVQKuVyOcY1oTi1U1uU4zqjEyc5amrFYDKZpcmSMiOZat9tFqVQaWyIQi8VgWRYH04hoLvX7fRSLRV9s0zQN+Xwe8Xh8ii0jogu1ED0T13VHJU521tKMRCIwTZNTy4horrmui42NjbEBNcMwRpsCERHNo2aziWKx6JuxEQ6HUSgUuLM20QKY64RzOK3Mtm3fPH9gUNjcNE1Eo1FOwSCiudZsNlEqlcZKOaXTaWSzWW4KRERzSSkF27axsbHhO57JZJDNZtl/I1oQc5lwKqVGJU527spoGAZM00Q8HmegIqK51u/3US6XxzY+C4fDsCyL9eeIaG71ej0Ui0W02+3RMV3XUSgUEI1Gp9gyItpvc5dwtlotVCoVX4ACBkFqWOKEiSYRzTOlFLa2tlCpVHzLBDRNg2marBlMRHOtXq9jfX3dF98ikQgKhQLXoRMtoLn5q+52u6hUKr56TMBgV8ZMJoN0Os1pZUQ09zqdDkql0tigWjweRy6XY2eMiOaW67qoVCpjVQRM00Q6neZAGtGCmvmeS6/Xg23bY3XmRATJZBKZTIYdMCKae67rwrZtVKtV3/FAIADLsjjFjIjmWrfbRbFYRKfTGR0zDAOFQgGRSGSKLSOiSZvZTM1xnFEtzZ0lTuLxOEzT5M5lRLQQGo0GSqWSb/MzEUE6nUYmk+HsDSKaa7VaDevr677+XCwWQz6fh67rU2wZER2EmUs4Xdcd1dLcWeIkGo3CNE1ulEFEC6Hf76NUKo0tFYhEIrAsi3WDiWiuua6LUqnkm6UmIjBNk3tuEC2RmUk4h5tk2Lbtq8MEAKFQCLlcjlMuiGghKKWwubk5VjtY0zTkcjkkEgl2xIhornU6HaytrfnKOQUCAaysrPDCAdGSmXrCqZRCo9FApVIZqzEXCARgmiZisRg7X0S0ENrtNkqlkm8dEwAkEgnkcjlOLyOiuTa8gFAul31TaBOJBCzL4hIBoiU01YRzWEtzZ8dL13Vks1lu/U9EC+N0uzMGg0FYlsUZHEQ09xzHwfr6um+ZgIjAsiwkk8kptoyIpmmqCWe9Xvclm5qmjWppcgSMiBZJq9XyJZvDhr+fkgAABmRJREFUkk6ZTIYDa0S0EKrVqi/ZDAaDWFlZ4Xp0oiU31YQzm82OFpKnUilkMhlOJyOihRSLxRCPx1Gv1xGNRmFZFnfaJqKFks1m0Ww20el0kEqlYJomLyAQ0XQTzmH9pXA4zFqaRLTwcrncKPHkVU0iWjQigkKhgG63i3g8Pu3mENGMmHqWx4BERMvCMAwkEolpN4OIaGKCwSCn0BKRD+c5EBERERER0UQw4SQiIiIiIqKJYMJJREREREREE8GEk4iIiIiIiCaCCScRERERERFNBBNOIiIiIiIimggmnERERERERDQRTDiJiIiIiIhoIkQptf8nFSkBeHHfT0xE8+6IUsqadiP2C2MdEZ0GYx0RLYM9xbqJJJxEREREREREnFJLREREREREE8GEk4iIiIiIiCaCCecUiYgjIo+KyBMi8g0RSe/TeY+KyBP7ca5ZIiJ3iMg3J3DewyLy5bO85qiI/N39/t1Ey4Cx7tww1hHNJ8a6c8NYtzyYcE5XSyl1k1LqegA2gH8y7QZNiojo027DbkTEUEq9qpR6/1leehQAAxPR+WGsmzLGOqIDwVg3ZYx1s4kJ5+z4MYCLAEBE4iLyXRF5WESOi8h7vONHReRJEfnvIvJTEblLRCLec7eIyGMi8mNsC3AiEhaRz3jneURE/rp3/CMi8jVvBO6EiPxTEflN7zX3i0h2ZwNF5LMi8p9F5D4ReV5E3u8dFxH5fW9E77iIfMA7foeIfF9E/heA4177nxKRP/Ze+2ci8gsicq+IPCMir/fe93rvdzzi/XzNmb44EXlARK7b9vgH3vex63m8z/4lEfkGgLu2jxx693/offcPi8hf8077uwDe6o1cflxEdO8z/5WIPC4i/+jc/8mJlhJjHWMd0TJgrGOsoyGlFG9TugGoez91AF8C8De9xwaApHc/B+BZAILBaEwfwE3ec18E8Pe8+48DeJt3//cBPOHd/+cAPuPdvxrASwDCAD7inTcBwAKwCeBj3uv+E4B/tkt7P+u1UwNwLYBnvePvA/Ad73MUvN9xCMAdABoAjnmvG7b/Bu8cDwH4tPfZ3gPga97rkgAM7/4vAPiKd/8OAN/cpV0fB/BJ7/4hAD8/y3k+AuAVANlt7Rp+X1EAYe/+lQB+stvvBvBRAP/Cux8C8JPh5+SNN978N8Y6xjreeFuGG2MdYx1vu98M0DRFRORRDP4wHsLgjxsY/KH+OxG5HYCLwQhZwXvuhFLqUe/+QwCOikgKQFopdbd3/HMAftG7/xYA/wUAlFJPiciLAK7ynvu+UqoGoCYimwC+4R0/DuDG07T5a0opF8DPRGTYprcA+LxSygFQFJG7AdwGYAvAg0qpE9vef0IpdRwAROSnAL6rlFIictz7HgAgBeB/iMiVABSAwGnaMvRFDL673wHwKxgEz7Od5ztKKXuXcwUA/FcRuQmAg1Pf1U53ArhxOBro/a4rAZw4zeuJlhljHWMd0TJgrGOso11wSu10tZRSNwE4AiCIU1MmPoTB6NQt3vNFDEavAKCz7f0OBqNmgsEf3m7kDL9/+7ncbY9d77xne4/s+Lmbxnn8zn+NQdC8HsAv4dRn35VS6iSAiojcCOADAL6wh/PsbNfQxzH4vl8L4FYM/l12IwB+XQ3WatyklDqmlLrrTO0kWmKMdYx1RMuAsY6xjnbBhHMGKKU2AfwGgN8SkQAGoyrrSqmeNzf/yFneXwWwKSJv8Q59aNvT9wwfi8hVAC4F8PQ+f4R7AHzAm/9uAbgdwIMXcL4UgJPe/Y/s8T1fAPAJAKnhSNt5nicFYNUb7ftVDKaTAEANg2kqQ98G8I+9fy+IyFUiEtvj7yBaSox1YxjriBYQY90Yxrolx4RzRiilHgHwGIAPAvgzALeKyE8wCCpP7eEUvwbgv8lgcXlr2/E/AKB7Uxv+N4CPKKU6u53gAnwVg7UGjwH4HoBPKKXWLuB8/wHAvxeRe3EqMJzNlzH47r54gef5AwAfFpH7MZh2MRwxexxAXwYL+D8O4I8B/AzAw97C9D/E6UcPicjDWOfDWEe0oBjrfBjrlpwodbor9kRERERERETnj1c4iYiIiIiIaCKYcBIREREREdFEMOEkIiIiIiKiiWDCSURERERERBPBhJOIiIiIiIgmggknERERERERTQQTTiIiIiIiIpoIJpxEREREREQ0Ef8fTw+51DnTxy0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1152x720 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.PrePlot(num=3, rows=2, cols=3)\n",
    "samples = MakeCorrelatedSamples()\n",
    "NormalPlotSamples(samples, ylabel='Sum of correlated exponential values')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Exercise:**    In Section 5.4, we saw that the distribution of adult weights is approximately lognormal. One possible explanation is that the weight a person gains each year is proportional to their current weight. In that case, adult weight is the product of a large number of multiplicative factors:\n",
    "\n",
    "w = w0 f1 f2 ... fn  \n",
    "\n",
    "where w is adult weight, w0 is birth weight, and fi is the weight gain factor for year i.\n",
    "\n",
    "The log of a product is the sum of the logs of the factors:\n",
    "\n",
    "logw = logw0 + logf1 + logf2 + ... + logfn \n",
    "\n",
    "So by the Central Limit Theorem, the distribution of logw is approximately normal for large n, which implies that the distribution of w is lognormal.\n",
    "\n",
    "To model this phenomenon, choose a distribution for f that seems reasonable, then generate a sample of adult weights by choosing a random value from the distribution of birth weights, choosing a sequence of factors from the distribution of f, and computing the product. What value of n is needed to converge to a lognormal distribution?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  }
 ],
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